The zoo is close to the airport.
Museo Ixchel and/or Popol Vuh on the same university campus, a 15 minute taxi ride from the airport.
I second the museums for the best time. They are great museums and priced well. I usually spend much more money at the book store at the museum!!!
Yes. The airport is practically inside the central part of the city as you will see. You will have more than enough time.
I would recommend going to walk around the historic area of Plaza Mayor. There's some interesting colonial architecture there, and it's a great place to people watch.
National Museum of Archaelogy. It's quite close to the airport. You can see the whole thing in an hour or so. It provides a good overview of Mayan history.
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